In recent years, various digital apparatuses such as compact disk players and digital audio tape recorders have been rapidly developed as commercial products. With this trend, techniques for converting digital signals into analog signals have become indispensable. DACs (digital to analog converters) are used for such conversion.
Where a digital amount is converted into an analog amount by a DAC, the analog voltage or current delivered from the DAC in response to the input assumes a "staircase" waveform which varies in a stepwise fashion.
For example, when a sinusoidal wave is produced, using the above-described DAC, digital codes of normally 8 to 16 bits which indicate displacements of the sinusoidal wave are applied to the DAC in response to every clock applied for conversion. The output waveform is a staircase wave S as shown in FIG. 1. The duration of each step of this staircase wave S is determined by the clocks described above.
As the ratio of the frequency of the clocks to the frequency of the desired sinusoidal waveform increases, the staircase wave S approximates more closely the actual sinusoidal wave F. However, the waveform S still maintains the staircase condition and, therefore, unwanted spurious signals are produced at and around the clock frequency and its harmonic frequencies.
Accordingly, it has been the common practice to connect a smoothing filter, or an analog filter, with the output of the DAC to smooth the staircase wave S, whereby the output waveform is made to approximate the sinusoidal waveform F. Where a desired output waveform is obtained, a filter having a sharp cut-off characteristic may be needed. However, it is not always practical to realize a filter having a sharp-cut-off characteristic. The prior art filter meeting these sharp cut-off requirements cannot always satisfy the phase and the gain characteristics of the passband. Additionally, the number of components is increased further to accommodate a sharp cut-off frequency.
Furthermore, where the frequency of the output sinusoidal wave is varied, filters having different cutoff frequencies are needed.